Conditioning belongs to the most important topics of any theory dealing with uncertainty. From the viewpoint of construction of Bayesian-network-like multidimensional models it seems to be inevitable. In evidence theory, in contrary to the probabilistic framework, various rules were proposed to define conditional beliefs and/or plausibilities (or basic assignments) from joint ones. Two of them — Dempster’s conditioning rule and focusing (more precisely their versions for variables) — have recently been studied in connection with the relationship between conditional independence and irrelevance and it has been shown, that for none of them conditional irrelevance is implied by conditional independence, which seems to be extremely inconvenient. Therefore we suggest a new conditioning rule for variables, which seems to be more promising from the viewpoint of conditional irrelevance, prove its correctness and also study the relationship between conditional independence and irrelevance based on this conditioning rule.